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MMO 083 Moscow MO 1941 self-intersecting closed broken line

Source:

July 18, 2019
geometry

Problem Statement

Consider △ABC\vartriangle ABC and a point MM inside it. We move MM parallel to BCBC until MM meets CACA, then parallel to ABAB until it meets BCBC, then parallel to CACA, and so on. Prove that MM traverses a self-intersecting closed broken line and find the number of its straight segments.
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